| Vanishing viscosity solutions of a $2 \times 2$ triangular hyperbolic system with Dirichlet conditions on two boundaries - Laura V. Spinolo We consider the $2 \times 2$ parabolic systems \begin{equation*} u^{\epsilon}_t + A(u^{\epsilon}) u^{\epsilon}_x = \epsilon u^{\epsilon}_{xx} \end{equation*} on a domain $(t, x) \in ]0, + \infty[ \times ]0, l[$ with Dirichlet boundary conditions imposed at $x=0$ and at $x=l$. The matrix $A$ is assumed to be in triangular form and strictly hyperbolic, and the boundary is not characteristic, i.e. the eigenvalues of $A$ are different from 0... Downloads: 3 | |

| Invariant Manifolds for Viscous Profiles of a Class of Mixed Hyperbolic-Parabolic Systems - Stefano Bianchini We are concerned with viscous profiles (travelling waves and steady solutions) for mixed hyperbolic-parabolic systems in one space variable. For a class of systems including the compressible Navier Stokes equation, these profiles satisfy a singular ordinary differential equation in the form \label{e:ab} dU / dt = F(U)/ z (U) . Here U takes values in $R^d$ and $F: R^d \to R^d$ is a regular function... Downloads: 2 | |

| Invariant manifolds for a singular ordinary differential equation - Stefano Bianchini We study the singular ordinary differential equation $$ \frac{d U}{d t} = f (U) / z (U) + g (U), $$ where $U \in R^N$, the functions $f \in R^N $ and $g \in R^N $ are of class $C^2$ and $z $ is a real valued $C^2$ function. The equation is singular in the sense that $z (U)$ can attain the value 0. We focus on the solutions of the singular ODE that belong to a small neighborhood of a point $\bar U$ such that $f (\bar U) = g (\bar U) = \vec 0$, $z (\bar U) =0$... Downloads: 2 | |

| Boundary layers for self-similar viscous approximations of nonlinear hyperbolic systems - Cleopatra Christoforou We provide a precise description of the set of residual boundary conditions generated by the self-similar viscous approximation introduced by Dafermos et al. We then apply our results, valid for both conservative and non conservative systems, to the analysis of the boundary Riemann problem and we show that, under appropriate assumptions, the limits of the self-similar and the classical vanishing viscosity approximation coincide... Downloads: 2 | |

| Accurate numerical schemes for approximating initial-boundary value problems for systems of conservation laws - Siddhartha Mishra Solutions of initial-boundary value problems for systems of conservation laws depend on the underlying viscous mechanism, namely different viscosity operators lead to different limit solutions. Standard numerical schemes for approximating conservation laws do not take into account this fact and converge to solutions that are not necessarily physically relevant. We design numerical schemes that incorporate explicit information about the underlying viscosity mechanism and approximate the physicall... Downloads: 2 | |

| A connection between viscous profiles and singular ODEs - Stefano Bianchini We deal with the viscous profiles for a class of mixed hyperbolic-parabolic systems. We focus, in particular, on the case of the compressible Navier Stokes equation in one space variable written in Eulerian coordinates. We describe the link between these profiles and a singular ordinary differential equation in the form $$ dV / dt = F(V) / z (V) . $$ Here $V \in R^d$ and the function F takes values into $R^d$ and is smooth... Downloads: 4 | |

| A uniqueness criterion for viscous limits of boundary Riemann problems - Cleopatra Christoforou We deal with initial-boundary value problems for systems of conservation laws in one space dimension and we focus on the boundary Riemann problem. It is known that, in general, different viscous approximations provide different limits. In this paper, we establish sufficient conditions to conclude that two different approximations lead to the same limit. As an application of this result, we show that, under reasonable assumptions, the self-similar second-order approximation and the classical visc... Downloads: 3 | |

| Drowning - Armin van Buuren
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| The Effect of Tidal Stripping on Composite Stellar Populations in Dwarf Spheroidal Galaxies - Laura V. Sales We use N-body simulations to study the effects of tides on the kinematical structure of satellite galaxies orbiting a Milky Way-like potential. Our work is motivated by observations of dwarf spheroidal galaxies in the Local Group, for which often a distinction is possible between a cold centrally concentrated metal rich and a hot, extended metal poor population. We find that an important attenuation of the initial differences in the distribution of the two stellar components occurs for orbits wi... Downloads: 2 | |

| Spectral stability estimates for the Dirichlet and Neumann Laplacian in rough domains - Antoine Lemenant In this paper we establish new quantitative stability estimates with respect to domain perturbations for all the eigenvalues of both the Neumann and the Dirichlet Laplacian. Our main results follow from an abstract lemma stating that it is actually sufficient to provide an estimate on suitable projection operators. Whereas this lemma could be applied under different regularity assumptions on the domain, here we use it to estimate the spectrum in Lipschitz and in so-called Reifenberg-flat domains... | |

| On the extension property of Reifenberg-flat domains - Antoine Lemenant We provide a detailed proof of the fact that any domain which is sufficiently flat in the sense of Reifenberg is also Jones-flat, and hence it is an extension domain. We discuss various applications of this property, in particular we obtain L^\infty estimates for the eigenfunctions of the Laplace operator with Neumann boundary conditions. We also compare different ways of measuring the "distance" between two sufficiently close Reifenberg-flat domains... | |

| Initial-boundary value problems for continuity equations with BV coefficients - Gianluca Crippa We establish well-posedness of initial-boundary value problems for continuity equations with BV (bounded total variation) coefficients. We do not prescribe any condition on the orientation of the coefficients at the boundary of the domain. We also discuss some examples showing that, regardless the orientation of the coefficients at the boundary, uniqueness may be violated as soon as the BV regularity deteriorates at the boundary. Downloads: 11 | |

| Some new well-posedness results for continuity and transport equations, and applications to the chromatography system - Luigi Ambrosio We obtain various new well-posedness results for continuity and transport equations, among them an existence and uniqueness theorem (in the class of strongly continuous solutions) in the case of nearly incompressible vector fields, possibly having a blow-up of the BV norm at the initial time. We apply these results (valid in any space dimension) to the k x k chromatography system of conservation laws and to the k x k Keyfitz and Kranzer system, both in one space dimension. Downloads: 1 | |

| Feedback and the Structure of Simulated Galaxies at redshift z=2 - Laura V. Sales We study the properties of simulated high-redshift galaxies using cosmological N-body/gasdynamical runs from the OverWhelmingly Large Simulations (OWLS) project. The runs contrast several feedback implementations of varying effectiveness: from no-feedback, to supernova-driven winds to powerful AGN-driven outflows. These different feedback models result in large variations in the abundance and structural properties of bright galaxies at z=2... Downloads: 2 | |

| The dark matter halos of dwarf galaxies: a challenge for the LCDM paradigm? - Ismael Ferrero The cold dark matter halo mass function is much steeper than the galaxy stellar mass function on galactic and subgalactic scales. This difference is usually reconciled by assuming that the galaxy formation efficiency drops sharply with decreasing halo mass, so that virtually no dwarf galaxies form in halos less massive than ~ 10^10 M_sun. In turn, this implies that, at any given radius, the dark mass enclosed by a galaxy must exceed a certain minimum... Downloads: 6 | |

| Disk galaxies at z=2 in OWLS - Julio F. Navarro We use the OWLS (OverWhelmingly Large Simulations) set of cosmological Nbody/gasdynamical simulations to study the properties of simulated galaxies at z=2. We focus on the effect of supernova feedback from evolving stars on the baryonic mass and angular momentum content of galaxies that assemble at the center of 1e11-3e12 h^{-1}M_\odot halos. Our main finding is that the mass and angular momentum of such galaxies are strongly coupled, in a way that is approximately independent of feedback: varyi... Downloads: 3 | |

| Clues to the "Magellanic Galaxy" from Cosmological Simulations - Laura V. Sales We use cosmological simulations from the Aquarius Project to study the orbital history of the Large Magellanic Cloud (LMC) and its potential association with other satellites of the Milky Way (MW). We search for dynamical analogs to the LMC and find a subhalo that matches the LMC position and velocity at either of its two most recent pericentric passages. This suggests that the LMC is not necessarily on its first approach to the MW, provided that the virial mass of the Milky Way is M_200 ~1.8e12... Downloads: 1 | |

| The Origin of Extended Disk Galaxies at z=2 - Laura V. Sales Galaxy formation models typically assume that the size and rotation speed of galaxy disks are largely dictated by the mass, concentration, and spin of their surrounding dark matter haloes. Equally important, however, are the fraction of baryons in the halo that collect into the central galaxy, as well as the net angular momentum that they are able to retain during its assembly process. We explore the latter using a set of four large cosmological N-body/gasdynamical simulations drawn from the OWL... Downloads: 5 | |

| Orbital Eccentricity as a probe of Thick Disk Formation Scenarios - Laura V. Sales We study the orbital properties of stars in four (published) simulations of thick disks formed by: i) accretion from disrupted satellites, ii) heating of a pre-existing thin disk by a minor merger, iii) radial migration and iv) gas rich mergers. We find that the distribution of orbital eccentricities are predicted to be different for each model: a prominent peak at low eccentricity is expected for the heating, migration and gas-rich merging scenarios, while the eccentricity distribution is broad... Downloads: 2 | |

| The Shape of Dark Matter Haloes in the Aquarius Simulations: Evolution and Memory - Carlos A. Vera-Ciro We use the high resolution cosmological N-body simulations from the Aquarius project to investigate in detail the mechanisms that determine the shape of Milky Way-type dark matter haloes. We find that, when measured at the instantaneous virial radius, the shape of individual haloes changes with time, evolving from a typically prolate configuration at early stages to a more triaxial/oblate geometry at the present day... Downloads: 2 | |

| The Origin of Disks and Spheroids in Simulated Galaxies - Laura V. Sales In the simplest scenario, disk galaxies form predominantly in halos with high angular momentum and quiet recent assembly history, whereas spheroids are the slowly-rotating remnants of repeated merging events. We explore these assumptions using one hundred systems with halo masses similar to that of the Milky Way, identified in a series of cosmological gasdynamical simulations GIMIC. At z=0, the simulated galaxies exhibit a wide variety of morphologies, from dispersion-dominated spheroids to pure... Downloads: 6 | |

| A Comparison of Galaxy Group Luminosity Functions from Semi-Analytic Models - Owain N. Snaith Semi-analytic models (SAMs) are currently one of the primary tools with which to model statistically significant ensembles of galaxies. The underlying physical prescriptions inherent to each SAM are, in many cases, different from one another. Several SAMs have been applied to the dark matter merger trees extracted from the Millennium Run, including those associated with the well-known Munich and Durham lineages... Downloads: 3 | |